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11—17 of 17 matching pages
11: 3.7 Ordinary Differential Equations
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►The method consists of a set of rules each of which is equivalent to a truncated Taylor-series expansion, but the rules avoid the need for analytic differentiations of the differential equation.
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12: 10.40 Asymptotic Expansions for Large Argument
13: 18.2 General Orthogonal Polynomials
14: 19.36 Methods of Computation
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►If the iteration of (19.36.6) and (19.36.12) is stopped when ( and being approximated by and , and the infinite series being truncated), then the relative error in and is less than if we neglect terms of order .
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15: 2.10 Sums and Sequences
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►In both expansions the remainder term is bounded in absolute value by the first neglected term in the sum, and has the same sign, provided that in the case of (2.10.7), truncation takes place at , where is any positive integer satisfying .
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16: 9.7 Asymptotic Expansions
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►In (9.7.5) and (9.7.6) the th error term, that is, the error on truncating the expansion at terms, is bounded in magnitude by the first neglected term and has the same sign, provided that the following term is of opposite sign, that is, if for (9.7.5) and for (9.7.6).
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17: 18.39 Applications in the Physical Sciences
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►For either sign of , and chosen such that , , truncation of the basis to terms, with , the discrete eigenvectors are the orthonormal functions
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